Want to work at Google? Answer these questions

This article was taken from the March 2012 issue of Wired
magazine. Be the first to read Wired's articles in print before
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It's famously tough getting through the Google interview process. But now we can
reveal just how strenuous are the mental acrobatics demanded from
prospective employees. Job-seekers can expect to face open-ended
riddles, seemingly impossible mathematical challenges and
mind-boggling estimation puzzles. William Poundstone, who deconstructed The Wolseley's menu for us, has collected
examples in his latest book, Are You Smart Enough to Work at Google?
(Oneworld).

1. You are shrunk to the height
of a 2p coin and thrown into a blender. Your mass is reduced so
that your density is the same as usual. The blades start moving in
60 seconds. What do you do?

Those who were paying attention in rocket-science class will
recall the formula for the energy of a projectile: E = mgh. E is
energy (of a bottle rocket, let's say), m is its mass, g is the
acceleration of gravity, and h is the height the bottle rocket
attains. The height increases in direct proportion with energy (as
long as mass stays the same). Suppose you tape two bottle rockets
together and light them simultaneously. Will the double rocket go
any higher? No; it's got twice the fuel energy but also twice the
mass to lift against gravity. That leaves the height, h, unchanged.
The same principle applies to shrunken humans jumping. As long as
muscle energy and mass shrink in proportion, jump height should
stay the same.

2. There's a latency problem in
South Africa. Diagnose it

"Latency problem in South Africa" is an inside joke at Google.
The phrase is intentionally equivocal techspeak, like a line in
science fiction. ("We're losing potency in our antimatter pods!")
The candidate should be able to figure out what it might mean,
though, and say something sensible. "Latency" means a delay. That
could apply to almost anything, from getting a marriage licence to
using public transit. It's a reasonable guess that a Google
interviewer is thinking about the internet. The interviewer could
mean either of the following:

• The internet is running slowly in South Africa.
• Google searches (only) are running slowly.

The ping operation measures latency on the Internet. A ping is a
dummy message sent from point A to point B and back. The time
interval is a measure of how fast information is flowing. By
pinging from many computers and stations in South Africa, you can
tell whether the Internet infrastructure is slow there. If not, the
problem may be with Google. Are there enough servers for the South
African traffic? Try a set of search terms from many points in
South Africa, to see whether all are slow or just some. This would
allow you to map the (imaginary) problem, and that generally
satisfies the interviewer.

3. Design an evacuation plan
for San Francisco

The 2006 Emergency Evacuation Report Card of the American
Highway Users Alliance gave Kansas City an A grade. New Orleans,
reeling from Katrina, got a D. San Francisco's grade? F. New York,
Chicago, and Los Angeles failed, too. The failing grades are due to
these cities' size, hemmed-in geography, and dependence on public
transportation. At such an environmentally conscious place as
Google, some interviewees instinctively talk up San Francisco's
public transit network. But most public transit runs within the
urban area. (BART, the San Francisco underground, can get people to
Oakland. Is that good enough? Or are we evacuating Oakland, too?)
Amtrak doesn't even stop in San Francisco proper. For the
foreseeable future, there's no such thing as a green evacuation.
Emptying a city on short notice means internal combustion engines
on public roads. Here are some bullet points to incorporate into
your plan:

• Make use of the fact that everyone wants to get out of the
city as fast as possible. Allow a marketplace of transportation
options. The biggest hitch in the Katrina evacuation was that New
Orleans authorities couldn't issue timely traffic advisories: they
simply didn't know which roads were jammed. Katrina hit the year
before Twitter and a couple of years before ubiquitous
smart-phones. Your plan should encourage people to tweet or text
about traffic conditions (but not while driving!) and should devise
a way to swiftly incorporate this information into social networks,
mapping applications, broadcast media, and so forth.

• Use school buses. The US's school buses have greater capacity
than all the modes of adult "mass transit" combined. Organise free
school bus shuttle service for those who don't have cars.

• Divert petrol to the region's petrol stations. There were fuel
shortages in the Katrina evacuation.

• In an authentic emergency, most people can't leave fast
enough, but you have to worry about three classes of stragglers:
those who refuse to go; those who can't evacuate without help
(they're disabled or in hospitals); and those so off the grid that
they won't hear about the evacuation (probably, many of them
homeless or elderly). As a legal and practical matter, there's not
much that can be done when a resident chooses to stay behind.
Efforts are better spent canvassing neighborhoods for people who
want to evacuate but need help. Put into service all the existing
dial-a-ride vans and ambulances, as they have special facilities
for the frail and disabled.

• Make sure some of the buses and trains allow pets and
suitcases. One reason people insist on staying behind is concern
for their pets and valuables.

• Designate all lanes of traffic arteries outbound. This allows
twice as much traffic and prevents the clueless from enter-ing the
city. Known as contraflow, this idea will be familiar to Bay Area
commuters. Since 1963, the Golden Gate Bridge has had reversible
lanes. In the mornings, four of the six lanes are inbound to San
Francisco. The rest of the time, there are three lanes each way, to
the city and the Marin County suburbs.

4. Using only a four-minute
hourglass and seven-minute hourglass, measure exactly nine
minutes.

With a four-minute hourglass, it's a cinch to measure four
minutes, eight minutes, 12 minutes, and so forth. The seven-minute
hourglass readily gives multiples of seven. You can measure still
other times by "adding" the two hourglasses -- starting one the
instant the other finishes. Let the four-minute glass run out, then
start the seven-minute glass. This gives 11 minutes total. Similar
strategies measure 15 minutes (4 + 4 + 7), 18 minutes (4 + 7 + 7),
and so on.

This method won't measure 9 minutes. But there's another trick,
"subtraction." Start both hourglasses simultaneously. The instant
the four-minute glass runs out, turn the seven-minute glass on its
side to stop the sand. There is then three minutes' worth of sand
in one bulb. That sounds promising. Nine is 3 X 3. But notice that
once you "use" the three minutes of sand, it's gone. You end up
with all seven minutes of sand back in one bulb. You could repeat
the whole process twice, but that doesn't permit measuring a
continuous nine minutes.

The way to remedy this is a third trick that might be called
"cloning." Start both glasses at zero minutes. When the nine-minute
glass runs out, flip it over. When the seven-minute glass runs out,
flip both glasses over. The four-minute glass, which had one minute
left to run, now has three minutes after the flip. When those three
minutes run out, flip over the seven-minute glass again. It will
then have three minutes of sand. (You've "cloned" the three minutes
that were in the small glass.) This gives a continuous nine
minutes.

The above is a good answer, just not the best one. Its defect is
that it requires 4 minutes of preparation time (to get 3 minutes of
sand in one bulb of the 7-minute glass). The scheme therefore takes
13 minutes total, in order to measure 9 minutes. Would you buy an
egg-timer that tool 4 minutes to warm up?

There is a solution that allows the timing to begin immediately.
Begin with the safe assumption that we're going to start both
hourglasses at 0 minutes. Then fast-forward to 7 minutes later. The
7-minute hourglass has just run out. The 4-minute glass has already
run out once and (presumably) has been flipped over. It should have
just 1 minute of sand remaining in its upper bulb.

All that's needed is to clone that 1 minute. At 7 minutes, flip
over the 7-minute glass. Let it run 1 minute, as measured by the
remaining sand in the 4-minute glass. That brings us up to the time
8 minutes. The 7-minute glass will have 1 minute of sand in its
lower bulb. Flip the 7-minute glass over again and let the minute
of sand run back. When the last grain falls, that will be 9
minutes.

5. Imagine a country where all
the parents want to have a boy. Every family keeps having children
until they have a boy; then they stop. What is the proportion of
boys to girls in this country?

Ignore multiple births, infertile couples, and couples who die
before having a boy. The first thing to realize is that every
family in the country has, or will have, exactly one boy when
they're done procreating. Why? Because every couple has children
until they have a boy, and then they stop. Barring multiple births,
"a boy" means one boy exactly. There are as many boys as completed
families.

A family can have any number of girls, though. A good way to
proceed is to take an imaginary census of girl children. Invite
every mother in the country to one big room and ask on the
public-address system: "Will everyone whose first child was a girl
please raise her hand?"

Naturally, one-half of the women will raise a hand. With N
mothers, N/2 would raise their hands, representing that many
firstborn girls. Mark that on the imaginary tote board: N/2.

Then ask: "Will everyone whose second child was a girl please
raise -- or keep raised -- her hand?"
Half the hands will go down, and no new hands will go up. (The
mothers whose hands were down for the first question, because their
first child was a boy, would not have had a second child.) This
leaves N/4 hands in the air, meaning there are N/4 second-born
girls. Put that on the tote board.

"Will everyone whose third child was a girl raise or keep raised
her hand?" You get the idea. Keep this up until finally there are
no hands still up. The number of hands will halve with each
question. This produces the familiar series

(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + . . .) xN

The infinite series sums to 1 (x N). The number of girls equals
the number of families (N) equals the number of boys (or very close
to it). The requested proportion of boys to girls is therefore 1 to
1. It's an even split after all.

6. Use a programming language
to describe a chicken

In 1968, the French writer and prankster Noël Arnaud published a
slim volume of poems in the computer language ALGOL (now obsolete,
it was a precursor of C). Arnaud restricted himself to ALGOL's
short dictionary of twenty-four predefined words. The poems were
not valid code. Describing a chicken in ALGOL, or C++, could be an
exercise in the same quixotic spirit.

Interviewers usually intend for you to describe an individual
chicken so that it might be distinguished from other members of its
species. Pretend you're starting a social network site for poultry.
"The chicken named Blinky is female, friendly, and dead."

Asked of Google engineers, this question prompts you to analyse
how an equation can be "beautiful" and then to give a suitable
example. The one certain thing about beauty is that it's
subjective. Even so, most conclude that a beautiful equation is
concise and of universal significance. Note, however, that you're
not just trying to think of a beautiful equation; you're trying to
impress the interviewer with your originality. It helps to give an
equation that the interviewer doesn't hear every day.

Most would agree this is a lame answer:

E = MC2

It's like a politician saying his favorite movie is Titanic.

You want Einstein? A better reply is:

G = 8πT

This packs the general theory of relativity into five
characters. G is the Einstein tensor, representing the curvature of
space-time. T is the stress-energy tensor, measuring the density of
mass and energy. The equation says that mass-energy curves space
and time (which curvature we experience as gravity).

Another five characters express much of quantum physics.

HΨ = EΨ

This is Schrödinger's equation, read as "the Hamiltonian of the
wave function equals its energy." The canonical Google answer is
Euler's equation. It connects five numbers central to mathematics:
e, pi, the imaginary number i -- and of course 1 and 0, which are
pretty important in the information business.

Eπi + 1 = 0

Euler's equation is regularly voted the "most beautiful
equation" or something of the kind. It was tied for first (with all
four Maxwell's equations!) in a 2004 Physics World poll for the
"greatest equations ever." As one reader put it, "What could be
more mystical than an imaginary number interacting with real
numbers to produce nothing?"

"Like a Shakespearean sonnet that captures the very essence of
love, or a painting that brings out the beauty of the human form
that is far more than just skin deep, Euler's equation reaches down
into the very depths of existence," the Stanford mathematician
Keith Devlin wrote. The best-known commentary of all is probably
that of Carl Friedrich Gauss, who said that unless this formula was
immediately obvious to a student, that student would never be a
first-rate mathematician.

You won't gain any points for originality by answering with
Euler's equation, though. It's like saying your favorite film is
Citizen Kane. The Gaussian integral has some of the same mystic
appeal, connecting e, pi, and infinity. One point in its favor:
Gauss didn't find it completely obvious.

The Gaussian integral also has something that Euler's equation
lacks -- relevance to life as we live it. The e-x2 is the Gaussian
function. A chart of it is the familiar bell-shaped curve of a
normal probability distribution. This is the "curve" that teachers
grade on -- the one that supposedly governs heights, IQ scores, and
the random walk of stock prices (but doesn't quite). The Gaussian
blur filter in Photoshop uses the same function to blur your ex out
of the picture.

In the equation, the integral computes the area under the
bell-shaped curve and finds it equal to the square root of pi, or
about 1.77. The equation can be viewed as a symbol of the role of
chance in the world. Many of the things we value most -- beauty,
talent, money -- are the result of scores of random factors,
ranging from genes to simple luck. When the factors determining a
quantity are truly random and additive, the quantity will follow a
normal distribution. Most people will be in the middle of the
curve. A few outliers will have a lot more or a lot less than the
mean. In 1886, Francis Galton said of this distribution:

"I know of scarcely anything so apt to impress the imagination
as the wonderful form of cosmic order expressed by the "law of
error." A savage, if he could understand it, would worship it as a
god. . . . Let a large sample of chaotic elements be taken and
marshalled in order of their magnitudes, and then, however wildly
irregular they appeared, an unexpected and most beautiful form of
regularity proves to have been present all along."

For the cult of the beautiful equation in all its delirious
glory, look no further than the British physicist Paul A. M. Dirac.
"It is more important to have beauty in one's equations than to
have them fit experiment," he once wrote. Dirac was notoriously
eccentric and socially awkward, partly the result of autism. As a
theoretical physicist, he saw the world as a puzzle to which
beautiful equations were the key. To a remarkable degree,
contemporary science (and many job interviewers) accept Dirac's
view of the world.

For an amusing rebuttal, see Richard Feynman in the second
volume of The Feynman Lectures on Physics, in which he makes the
amazing claim that all of physics can be reduced to a single
equation. The equation is:

U = 0

That's it! That's everything about the universe! Feynman was
half-serious. Take an equation like E = MC2. It is said to be deep.
Its so-called beauty rests with the fact that it explains so much
with just a few marks on paper, a few black pixels on white. This
perception of simplicity rests on hard-won and messy concepts,
Feynman argued. What is energy? What is mass? What is the speed of
light? None of these concepts existed for al-Khwarizmi or Leonardo
da Vinci. Energy and mass had only started to gel by Newton's time.
"The speed of light" was hardly a scientific matter until the
nineteenth century. Feynman's point is that E = MC2 is an
abbreviation. Admire it, just don't get wrapped up in how "simple"
it is. It's not all that simple.
Notice that you can transform Einstein's equation into:

E - MC2 = 0

All I've done is to subtract MC2 from both sides. They were
equal before, and they must be equal now. Now square both sides of
the equation. This gives:

(E - MC2) 2 = 0

The point of this will become clear in a moment. It's part of
Feynman's recipe for the ultimate beautiful equation. Blend in a
few more equations. For the heck of it, we'll use Schrödinger's
equation and Euler's equation. Leave Euler's as is and tweak
Schrödinger's:

eπi + 1 = 0

HΨ - EΨ = 0

Then square both sides of each and add to Einstein's rejiggered
equation

(E - MC2)2 + (HΨ - EΨ)2 + (eπi + 1)2 = 0

All three terms on the left have to be 0 (say Einstein,
Schrödinger, and Euler). The equation must be correct, assuming its
three components are. Furthermore, the only way the equation can be
correct is if all the terms are 0. (That's the point of the
squaring. It guarantees that no term could be negative. The only
way for three nonnegative terms to add up to 0 is for all to be
0.)

Don't stop there. Throw in the kitchen sink, said Feynman. All
equations, great and trivial, can be put in this form and appended
to the left side of this master equation. Feynman called the
quantities on the left UN, where N ranges from 1 to as far as you
care to go. Sum them up and you have simply U, standing for
unworldliness. It is a measure of anything and everything that
doesn't fit into the scheme of physics. The master equation says
the unworldliness is 0. You can unpack all of physics from
this.

U = 0 is simpler (more "beautiful") than any other equation. It
says everything the other equations do, and it's as simple as an
equation can possibly get. An equation means you've got an equals
sign, with one thing on the left of it, and one thing on the right.
Three characters is the bare minimum, and U E 0
delivers that beautiful (anorexic?) limit.

Feynman's real point was that "U = 0" is a silly kludge serving
no purpose except to say everything about the universe as concisely
as possible! Feynman was asking, are you sure that's what you mean
by beautiful? It's worth thinking about. A good answer to this
interview question might start with Feynman's U = 0. Then, if you
think you've got a better notion of what "beauty" is, describe it
and tell what equation best fits it.

8. You want to make sure that
Bob has your phone number. You can't ask him directly. Instead you
have to write a message to him on a card and hand it to Eve, who
will act as a go-between. Eve will give the card to Bob and he will
hand his message to Eve, who will hand it to you. You don't want
Eve to learn your phone number. What do you ask Bob?

Even if you give the short, simple answer you may be asked to
supply the RSA answer, too. It's not that complicated as long as
Bob has a computer and can follow directions. You might ask the
interviewer about Bob's maths and computer skills.
With RSA, each person generates two keys, a public one and a
private one. A public key is like an e-mail address. It allows
anyone to send you a message. A private key is like your e-mail
password. You need it to get your e-mail messages, and you must
keep it secret -- otherwise, anyone could read your mail. You won't
be able to send Bob a secret message because he hasn't set up his
keys. He may not know what RSA is until you tell him! But you don't
need to send Bob a secret message. You want Bob to send you a
secret message, namely your phone number. This means that you need
keys for yourself, not for Bob. The outline of the solution is
this:

Hey, Bob! We're going to use RSA cryptography. You may not know
what that is, but I'll explain exactly what you have to do. Here is
my public key. . . . Take this and my phone number and produce an
encrypted number by following these directions. . . Send that
encrypted number back to me, via Eve.

The trick is to word the instructions so that almost anyone can
do it. You also have to be concise. RSA cryptography was first
described, it now appears, in 1973. Its original inventor was the
British mathematician Clifford Cocks, who worked for Her Majesty's
secret service. His scheme was considered impractical: it required
a computer, of all things. That was not easy to come by when spies
generally had to make do with cameras hidden in cuff links. Cocks's
idea was classified until 1997. Meanwhile, in 1978 three MIT
computer scientists independently came up with the same idea. The
last initials of the MIT group -- Ronald Rivest, Adi Shamir, and
Leonard Adelman -- supplied the acronym.

In the RSA system, a person who wants to receive messages must
pick two random prime numbers, p and q. The numbers must be large
and at least as big (in digits) as the numbers or messages being
transmitted. For a phone number of ten decimal digits, p and q each
should be at least ten digits.

One way to choose p and q is to Google a website that lists
large prime numbers. The Primes Pages, run by Chris Caldwell of the
University of Tennessee at Martin, works well. Pick two ten-digit
primes at random. Here are two:

1,500,450,271 and 3,367,900,313

Call these p and q. You have to multiply them and get the exact
answer. This is a little tricky. You can't use Excel or Google
calculator or most other consumer software because they show a
limited number of significant figures. One option is to multiply by
hand. An easier one is to use Wolfram Alpha
(www.wolframalpha.com):

Just type in:

1500450271 * 3367900313

and it will give the exact answer:

5053366937341834823

Call this product N. It's one component of your public key. The
other component is a number called e, an arbitrarily chosen number,
ideally of length equal to N, that does not divide evenly by (p -
1)(q - 1). I may have lost you with that last part, but don't
worry. In many applications, coders simply pick 3 for e. This is
good enough for most purposes, and it permits fast enciphering.

Having chosen N and e, you're good to go. You just need to send
those two numbers to Bob, along with the Complete Idiot's Guide to
RSA Cryptography. Bob has to compute:

xe mod N

Where x is the phone number. Since we've chosen 3 for e, the
part on the left is x cubed. It will be a thirty-digit number. The
"mod" indicates modulo division, meaning that you divide x3 by N
and take only the remainder. This remainder must be in the range of
0 to N  1. Thus it's probably going to be a twenty-digit number.
This twenty-digit number is the encrypted message that Bob sends
back to you. Bob therefore needs to be able to cube a number and do
long division. The crucial part of the instructions could say

Bob, I need you to follow these instructions carefully with-out
questioning them. Pretend my phone number is a regular ten-digit
number. First, I need you to cube the number (multiply it by itself
and then multiply the product by the original number again). The
answer, which will be a thirty-digit number, has to be exact. Do it
by hand if you have to, and double-check it. Then I need you to do
the longest long division you've ever done. Divide the result by
this number:

5,053,366,937,341,834,823. The division also has to be exact.
Send me the remainder of the division only. It's important that you
don't send the whole part of the quotient -- just the
remainder.

Bob, go to this website: www.wolframalpha.com. You'll see a
long, rectangular box outlined in orange. Type my ten-digit phone
number into the box, without using dashes, dots, or parentheses --
just the ten digits. Immediately after the phone number, type
this:

ˆ3 mod 5053366937341834823

Then click the little equals sign in the right of the box. The
answer, probably a twenty-digit number, will appear in a box
labeled "Result." Send that answer, and only that answer, to
me.

Naturally, Eve reads these instructions, and she also reads
Bob's reply. She can't do anything with it. She's got a
twenty-digit number that she knows is the remainder when the cube
of the phone number is divided by 5,053,366,937,341,834,823. Nobody
has yet figured out an efficient way to recover the phone
number.

How are you any better off? You are because you have the secret
decoder key. This, d, is the inverse of e mod (p - 1)(q - 1). There
is an efficient algorithm for calculating that -- provided, of
course, that you know the two primes, p and q, that were used to
generate N. (You know them because you picked them, remember?) Call
Y the encoded number/message Bob sends back. His original message
is:

Yd mod N

To figure this, you just type it into Wolfram Alpha (replacing
Y, d, and N with the actual numbers).

Eve knows N, since it was on the card you asked her to give to
Bob. She knows y, since it was Bob's reply to you. But she doesn't
know d, and she has no way of learning it. Eve has algorithm
trouble. It is easy to multiply two numbers -- heck, they teach
that to schoolkids. It is hard to factor a large number.

9. A man pushed his car to a
hotel and lost his fortune. What happened?

He was playing Monopoly.

10. If you had a stack of
pennies as tall as the Empire State Building, could you fit them
all in one room?

This may sucker you into thinking that it is one of those
interview questions where you're intended to estimate an absurd
quantity. Hold on -- the question doesn't ask how many pennies. It
asks, will the stack fit in a room? The interviewer wants a
yes-or-no answer (with explanation, of course).

That should be a clue, as should the fact that the question
doesn't say how big the room is. Rooms come in all sizes.
Intuition might suggest that the stack wouldn't fit in a phone
booth but would fit easily in the Hall of Mirrors at
Versailles.

The answer is roughly this: "The Empire State Building is about
a hundred stories tall [it's 102 exactly]. That's at least a
hundred times taller than an ordinary room, measured from the
inside. I'd have to break the skyscraper-high column of pennies
into about a hundred floor-to- ceiling-high columns. The question
then becomes, can I fit about a hundred floor-to-ceiling penny
columns in a room? Easily! That's only a ten-by-ten array of penny
columns. As long as there's space to set a hundred pennies flat on
the floor, there's room. The tiniest New York apartment, an
old-style phone booth, has room."
Swagger counts. The goal is not just to get the right answer but
to make it look easy. Great athletes do this naturally. Lately, job
seekers are expected to do the same.

Comments

This is really interesting stuff, it reminds me of a piece of information given to me on a walking tour of Oxford; All Souls College is an invitation only graduate college, and is credited as having the most difficult entrance exam/interview of all the Oxford colleges. Candidates will typically be presented with one word exam questions (amongst other questions), e.g. 'Ethics' and expected to give a suitable, and no doubt erudite, response.

Phil

Apr 11th 2012

I suspect there aren't wrong answers to many of the questions, they are wanting to find out how your mind works, can it make sensible approximations and can you base robust conclusions based on those. A certain amount of general knowledge always helps get the right order of magnitude for calculations and self checking.

Jono

Apr 11th 2012

Just a note to say that you don't need to let a mechanical watch wind down to stop it, just pull out the crown.

roger

Apr 12th 2012

Sorry you've got Question 5 wrong there. The logic to calculate the number of girls to boys born is correct but you've forgotten to add the parents into the equation.

NickyB

Apr 12th 2012

In reply to NickyB

A pair of child bearing parents will be a man and a woman for sake of convenience. It can also be noted that a man is not a boy, nor is a woman a girl.

PatHeist

May 4th 2012

In reply to NickyB

1Man+1Women= (>=1child)so if we add parents to the equation, it will remain same, balancing on both of the sides!

Sravan sai

Sep 11th 2012

In reply to NickyB

The question asked about the ratio of girls to boys, not male to female. And the ratio will still be 1:1 even if we count parents.

shashank nagamalla

Dec 5th 2012

So now they just reprint the questions from the books about getting a job at Microsoft, and change one word in the title.

Mike

Apr 14th 2012

You might want to check your answer to this question:Using only a four-minute hourglass and seven-minute hourglass, measure exactly nine minutes.

In your answer you talk about using a 9 minute hourglass... if there was a 9 minute one available... just use that one duuurrr!

Tinker

Apr 14th 2012

I see now I made a mistake in previous comment while energy in muscles proportional also to mass not the cross section, the nice explanation of many issues and example of data are in the book books.google.pl/books?id=8WkjD3L_avQC "The conclusion is that similar animals of different masses should jump to the same height provided that their muscles contracts with the same force" (p.177-179)

W13

Apr 14th 2012

I'm an engineer at Google, and this is wildly inaccurate. We ask questions about programming and algorithms, not questions like this.

Kelly

Apr 14th 2012

In reply to Kelly

sir,,how to apply for google.i am soft engg. In india.(just passed)

niks

Jun 12th 2012

In reply to Kelly

Hii, so how can i work at google as well as i'm an Assistant Lecturer in the faculty of computer science!! thxx

saby

Jan 10th 2013

I interviewed at Google last year, and in fact have another interview coming up. None of these questions were asked before and I don't anticipate them being asked again. Like Kelly said, it's about algorithms and programming languages for the engineering job. I don't doubt there are some fringe jobs that might have these questions though.

Secondly, moduli up to 768 bits have been publicly factored for something like a decade, and a 20 bit modulus could be factored on a desktop machine in no time- on mine, your example factorizes in less than 3 seconds. This means that from the public key I can obtain your private key- a total break.

This leads me to the fourth problem in your example: using textbook RSA. RSA is widely known in the security community to be insecure without use of an appropriate padding method (eg, OAEP), which could almost certainly not be performed by hand.

Problem number five is that you assume Eve can't modify what's written on the card, or exchange it for another card. If this were the case, she would just hand Bob a card with a public key she generated on it, let Bob run through the rigamarole, and decrypt it (obtaining your phone number) then re-encrypt it under the key you gave so you wouldn't know it was intercepted.

Finally, the set of 7-digit phone numbers can be trivially enumerated on a computer. All Eve would have to do would be to write a script that performed the same operation Bob did for every possible phone number and then stop when it matched the one he wrote back, and she would still get your phone number- no trickiness required.

Also, +1 to Kelly's comment.

G

Apr 14th 2012

In reply to G

Since part of the example got swallowed by a lame attempt to prevent XSS, let me restate it:Thirdly, even if you correctly chose a large random modulus (>2048 bits) the value you're encrypting is less than 25 bits. This means that m^3 will be very small relative to the modulus (~75 bits). Because of this, all an attacker needs to do is take the cube root of the ciphertext (over the integers) to decrypt it.(The remainder of the example stands)

G

Apr 15th 2012

I interviewed at Google last year, and in fact have another interview coming up. None of these questions were asked before and I don't anticipate them being asked again. Like Kelly said, it's about algorithms and programming languages for the engineering job. I don't doubt there are some fringe jobs that might have these questions though.

Sim

Apr 15th 2012

That's not true. I had an interview at Google and the only question they asked me was why I was late.

krystian

Apr 15th 2012

In reply to krystian

why were you late to an interview with google ?????????????????????????????

jordi

Apr 18th 2012

When I interviewed at Google, they asked me how many tennis balls would it take to completely fill a room.I suck at Math, which resulted in my incoherently blabbering some random formula. Needless to say, I didn't get the job.

why cloning minutes with sandglasses.measure one minute as explained let it run and then just flip the four minute hourglass twice giving 4+4+1=9

x

Apr 28th 2012

In reply to x

To get sand worth 1 minute in the bowl, you have to take 7 minutes. As per your method it would take 7+(1+4+4)=16 minutes from starting. That means you have to wait 7 minutes to get sand worth 1 minute in the bowl and then start counting 9 minutes. By the given method , it would take 7 minutes required to get sand worth 1 minute in the bowl + 1 minute that you cloned twice = 9 minutes exactly from start to measure 9 minutes..